It is easy to see that Assumptions REF  and REF 
are required for using Proposition REF . The remaining condition
to show is that \({Y\vert A=a,Z=\cdot }\)  is in \(N(E_{a}^{*})^{\perp }.\) 
We show that the structural assumption (Assumption REF ) and completeness assumption (Assumption REF ) imply the required condition.
The result below closely follows [1]} in that we share the same completeness condition.
